Morley’s Trisector Theorem

• Autorzy: Roland Coghetto
• Języki publikacji: EN

Abstrakty

EN

Morley’s trisector theorem states that “The points of intersection of the adjacent trisectors of the angles of any triangle are the vertices of an equilateral triangle” [10]. There are many proofs of Morley’s trisector theorem [12, 16, 9, 13, 8, 20, 3, 18]. We follow the proof given by A. Letac in [15].

Słowa kluczowe

EN

Euclidean geometry; Morley’s trisector theorem; equilateral triangle

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2015
• Tom: 23
• Numer: 2
• Strony: 75-79

Daty

wydano

2015-06-01

otrzymano

2015-03-26

online

2015-08-13

Twórcy

autor

Roland Coghetto

• Rue de la Brasserie 5 7100 La Louvière, Belgium

Bibliografia

• [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
• [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
• [3] Alexander Bogomolny. Morley’s miracle from interactive mathematics miscellany and puzzles. Cut the Knot, 2015.
• [4] Czesław Bylinski. Functions and their basic properties. Formalized Mathematics, 1(1): 55-65, 1990.
• [5] Czesław Bylinski. Introduction to real linear topological spaces. Formalized Mathematics, 13(1):99-107, 2005.
• [6] Czesław Bylinski. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
• [7] Roland Coghetto. Some facts about trigonometry and Euclidean geometry. Formalized Mathematics, 22(4):313-319, 2014. doi:10.2478/forma-2014-0031.
• [8] Alain Connes. A new proof of Morley’s theorem. Publications Math´ematiques de l’IH ´ES, 88:43-46, 1998.
• [9] John Conway. On Morley’s trisector theorem. The Mathematical Intelligencer, 36(3):3, 2014. ISSN 0343-6993. doi:10.1007/s00283-014-9463-3.
• [10] H.S.M. Coxeter and S.L. Greitzer. Geometry Revisited. The Mathematical Association of America (Inc.), 1967.
• [11] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
• [12] Cesare Donolato. A vector-based proof of Morley’s trisector theorem. In Forum Geometricorum, volume 13, pages 233-235, 2013.
• [13] O.A.S. Karamzadeh. Is John Conway’s proof of Morley’s theorem the simplest and free of A Deus Ex Machina ? The Mathematical Intelligencer, 36(3):4-7, 2014. ISSN 0343-6993. doi:10.1007/s00283-014-9481-1.
• [14] Akihiro Kubo and Yatsuka Nakamura. Angle and triangle in Euclidean topological space. Formalized Mathematics, 11(3):281-287, 2003.
• [15] A. Letac. Solutions (Morley’s triangle). Problem N 490. Sphinx: revue mensuelle des questions r´ecr´eatives, 9, 1939.
• [16] Eli Maor and Eugen Jost. Beautiful geometry. Princeton University Press, 2014.
• [17] Robert Milewski. Trigonometric form of complex numbers. Formalized Mathematics, 9 (3):455-460, 2001.
• [18] Cletus O. Oakley and Justine C. Baker. The Morley trisector theorem. American Mathematical Monthly, pages 737-745, 1978.
• [19] Marco Riccardi. Heron’s formula and Ptolemy’s theorem. Formalized Mathematics, 16 (2):97-101, 2008. doi:10.2478/v10037-008-0014-2.
• [20] Brian Stonebridge. A simple geometric proof of Morley’s trisector theorem. Applied Probability Trust, 2009.
• [21] Andrzej Trybulec and Czesław Bylinski. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.
• [22] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
• [23] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1 (1):73-83, 1990.
• [24] Yuguang Yang and Yasunari Shidama. Trigonometric functions and existence of circle ratio. Formalized Mathematics, 7(2):255-263, 1998.

Identyfikatory

DOI

10.1515/forma-2015-0007